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Understanding Regressions with Observations Collected at High Frequency over Long Span

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  • Chang, Yoosoon
  • Lu, Ye
  • Park, Joon Y.

Abstract

In this paper, we analyze regressions with observations collected at small time interval over long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast relative to T → ∞. Such a phenomenon is indeed what is frequently observed in practice for the type of regressions considered in the paper. In contrast, our asymptotic theory predicts that the spuriousness disappears if we use the robust version of the Wald test with an appropriate longrun variance estimate. This is supported, strongly and unambiguously, by our empirical illustration.

Suggested Citation

  • Chang, Yoosoon & Lu, Ye & Park, Joon Y., 2018. "Understanding Regressions with Observations Collected at High Frequency over Long Span," Working Papers 2018-10, University of Sydney, School of Economics.
  • Handle: RePEc:syd:wpaper:2018-10
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    File URL: http://econ-wpseries.com/2018/201810.pdf
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    References listed on IDEAS

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    1. Kim, Jihyun & Park, Joon Y., 2017. "Asymptotics for recurrent diffusions with application to high frequency regression," Journal of Econometrics, Elsevier, vol. 196(1), pages 37-54.
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    1. Papers of the Moment
      by Francis Diebold in No Hesitations on 2019-01-07 13:50:00

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    Cited by:

    1. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2018. "Testing for Stationarity at High Frequency," Working Papers 2018-09, University of Sydney, School of Economics.

    More about this item

    Keywords

    high frequency regression; spurious regression; continuous time model; asymptotics; longrun variance estimation;

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